E Board: Suggested Books ICSE Board: Foundation Mathematics Class 8: Reference Books Class 8: NTSE Preparation --------------------------------------------------------------

Q.1 Two angles of a triangle measure . Find the measure of the third angle.

Answer:

Sum of all the angles of a triangle

Let the third angle

Therefore

Or

Q.2. Three angles of a triangle are in the ratio of 2 : 5 : 8. Find the angles of the triangle.

Answer:

Let the angles be

Therefore

Or

Therefore the angles are

Q.3. One angle of the triangle is and the other two angles are equal. Find the measure of each angle of the triangle.

Answer

Let the two equal angles be

Therefore

Or

Therefore the angles are

Q.4. One angle of the triangle is and the other two angles are in the ratio . Find the measures of each of the unknown angles.

Answer:

Let the two unknown angles be

Therefore

Or

Or

Therefore the two angles are

Q.5. Three angles of a triangle measures . Find the value of and the measures of all the angles.

Answer

Or

Hence the angles are

Q.6. In . Find the value of and the measure of all the angles of the triangle.

Answer:

or

Hence

Q.7. In . Find the value of x and the measure of all the angles of the triangle and show that the triangle is an isosceles triangle.

Answer:

Hence

Q.9. In . Find the angles of the triangle.

Answer:

Let

Q.10. In the adjoining figure, it is given that . Find the value of $latex .

Answer:

Note: Sum of angles of adjacent angles on a straight line

Note:Sum of all angles of a triangle

Q.11. In the adjoining figure, it is given that and are bisectors of respectively. Find the measure of

Answer:

Let

Since

Q.12. Using the information given in the adjoining figure, find the value of

Answer:

Q.13. In the adjoining figure, DCBE is a straight line, . Find

Answer:

Therefore

Q.14. Find, giving reasons, the unknown angles marked by in the following figures.

Answer:

i)

iii)

iv)

v)

vi)

Given which means

Q.15. In the adjoining figure, if , find the value of and hence, find the measure of

Answer:

Q.16. In , side AC has been produced to D. If , find the measure of

Answer:

Let

Therefore

Q.17. In the adjoining figure, it is given that: . Find the measure of

Answer:

i)

Note:Co-interior Angles

ii)

Q.18. In the adjoining figure, it is given that:. Find

Answer:

Therefore

i) & ii) Hence

iv)

iii)

Q.19. Using the information given in the adjoining figure, calculate the values of

Answer:

In

In

Q.20. Sides have been produced to D and E respectively. are bisectors of respectively. If , find the measure of

Answer:

Given

Q.21. In the adjoining figure, it is being given that . Find the value of .

Answer:

Note:Alternate angles

Q.22. In the adjoining figure, it is being given that . Find the value of .

Answer:

In

In

Q.23. In the adjoining figure, it is given that Find the value of

Answer:

In $latex \Delta FEC, 90+42+(180-z)=180 &s=1$

In

In

Q.24. In the adjoining figure,

Answer:

In

Since

Note:Alternate Angles

Substituting ii) in i) we get

Substituting the value of

Q.25. In the adjoining figure, . Find the values of

Answer:

In

Since

Substituting ii) in i) we get

Substituting in ii) we get

E Board: Suggested Books ICSE Board: Foundation Mathematics Class 8: Reference Books Class 8: NTSE Preparation --------------------------------------------------------------